The process of fiting some statistical model to a particular set of data. Mostly done on a computer, and using varied numerical methods such as optimization or numerical integration, or simulation.

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8 views

Standard to weight by x/(sigma^2)

I have a function $f$ that I am trying to fit with $\{x_i, y_i, \sigma_i\}$ where $\sigma_i$ is the standard deviation of $y_i$ at $x_i$. It is of great importance that $f$ reflect $y$ asymptotically ...
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11 views

Case control sampling - matching distribution

I have large number of observations (say few thousands) which are divided into two groups A and B. I am interested in conducting ...
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10 views

Estimating Distributions of Weighted Data

I'm trying to build a bivariate copula-based model of income and wealth in Italy and I'm having trouble handling weighted data. I have access to micro data, a survey of about 10,000 households that ...
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17 views

Reg-Arima fitted estimates more flexible than forecast

I am fitting a regression model with ARMA errors, and comparing its fitted and forecasted values with a linear regression. I am wondering why a reg-ARMA appears to have a much better fitted estimate ...
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10 views

Fit a straight line in 3D with 3D uncertainties

So I'm trying to extend the recipe given here in chapter 7 to 3 dimensions. I have x,y,z data points each with their own uncertainties and I'm trying to fit a straight line. So I'm extending the the ...
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19 views

Which model(s) are appropriate for this kind of data

So, I tried to implement a model on some data. The dependent variable is a ratio that can get higher than 1, is lower bounded by zero and, seeing figure 1, is left skewed.Thus, a logit regression is ...
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9 views

Compare inferred parameters

Given one set of data I fit the same model in two different ways. I now have the inferred values for the parameters and the standard error. How can I test if they are statistical different? I have ...
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36 views

Linear Regression Analysis with heavy tailed noise

I have 5 data sets, each can be fitted (this is given) with a linear model $y=a+x b+\epsilon$ but of different parameters $a,b$, where $\epsilon$ is a heavy-tailed noise of mean zero and $x$ ...
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10 views

How to select the thresold in Generalized Pareto distribution

I'm using generalized Pareto distribution to fit the tail data, I want to know is there any computational way to estimate the threshold parameter as we do in estimating the sigma et shape using MLE? ...
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25 views

fitting t distribution with lighter tails

I am trying to fit a t distribution in R using the fitdistr function in the MASS package as follows ...
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14 views

How to determine which factor rotation gives the best model fit? [duplicate]

I have to use factor analysis to determine if it fits my data adequately. I am wondering how rotations play into it. What am I looking for when I change the rotation? The p-value is the same so how I ...
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1answer
33 views

Confidence bound of fitted function

I'm dealing with fitting function to data set and with interpretation of such fit and I'm working with Matlab 2011b. Suppose we have fitted function in form $y=f(a_i,x_j)$ where $a_i$ are parameters ...
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45 views

Error in Linear Regression Parameters: Using mean measurement vs. all measurements

I have a set of measurements y taken at 17 different values of x, with 50 repeated measurements at each value of x. They follow a simple linear relationship y = mx + c, and I am fitting the parameters ...
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1answer
37 views

Single fitted parameter from multiple data

Let's say I have to perform more than one non-linear fit over experimental replicates, each of them being an exponential decay (y <- 50*exp(-Ax)). What I'm doing ...
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22 views

optim() convergence in fitting gamma distribution to separate peaks of time series data

Trying to fit gamma distribution to each separate peak of time series data (chromatography). As a peak i take local minimum-maximum-minimum part of the data each time. Since the peaks values do not ...
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24 views

Fit raw data to distribution and use chi-square

I have a dataset of number of tweets over time similar to this: ...
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1answer
130 views

How do you fit a Poisson distribution to table data?

I've been given a table of $x=(0,1,2,3,4,5,6)$ and $y=(3062,587,284,103,33,4,2)$, which are such that the number of $x_i$ tells an amount of children that all $y_i$s have. I'm asked to fit a Poisson ...
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24 views

Visualizing 3-D fit

I have two independent variables, call them X and Y, and I have to fit a dependent variable Z = f(X,Y) somehow. In an experiment, the experimentalist measured Z as a function of X, and another ...
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1answer
44 views

model fit in logistic regression

I have developed a model for simple logistic regression with 1 independent ordinal variable and 4 binary independent variables. The model gives 64% correctly predicted cases, a Nagelkerke r2 of 12% ...
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20 views

Fitting Neural Network or Radial Basis Function to 2D surface

I am trying to fit both a neural network and radial basis functions to a 2D plot that presents a pronounced peak. However, the neural network is unable to reach the magnitude of the peak, while the ...
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22 views

When to use weighting in least squares?

Normally when one talks about weighted least squares, the end-goal is to weight each point by its variance. However my question pertains to models which have multiple components. It will be easier ...
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32 views

How to test model fit (residuals?) for a linear regression with a binomial independent variable?

This must be common knowledge and asked so many times, but I can't find it. I'm a bit of a rookie, so my apologies if it's a redundant question. I am doing a linear regression with a binomial ...
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16 views

Relationship between T, the Adjustment Rate, and Power for an Autoregressive Unit Root

So I have a question related to autoregressive unit roots. This picture shows a graph for c and n with power = .9 in blue and power = .8 in red. Any ideas what could be used to fit this graph or ...
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1answer
67 views

In R how can I fit multivariative distribution to data and sample from it?

I collected data on post parcells delivery, each object is a combination of 3 variables: Weight (continuous >0) Destination city (categorial - factor of hundreds) Delivery type (categorial - ...
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1answer
28 views

Fitted GARCH conditional mean values lag by 1

I am attempting to calculate the RMSE in-sample value from a GARCH model. ...
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15 views

Deleting outliers in (almost) uniform graph

I wrote an algorithm that finds the centroids of rectangles which are on the same line and groups these rectangles together. I know that only those rectangles with a roughly equal size belong ...
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29 views

Chi square statistic when both model and data have errors

I have written a code which fits a model to some data. My model and data are two-dimensional images. To be more precise, I am fitting some kind of galaxy model to astronomical observations. The ...
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15 views

Prediction interval of 3d data

I have a data set consisting of 3 columns: $x$, $y$ and $z$. I am analyzing the influence of $x$ and $y$ on $z$: I have managed to find a surface fit of the form $z=10^{a+bx+cx^2+d\log{y}}$ in ...
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25 views

Fitting a glm in practice

This question will be a little wordy - I'll try to summarize at the end. I'm currently working on a machine learning library and I'm implementing GLMs. To fit my models I've been implementing an ...
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17 views

Interpreting the Fisher Information Matrix

I'm studying the proprieties of two different models, used to fit some data. My physical process is such that $y=f(a,b)$. $y,a$ and $b$ are vectors (quite large ones actually). Model one takes $a$ as ...
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28 views

Support of distribution (distribution fitting)

This might be a weird question. I want to know why Matlab still run to produce estimated parameter whenever I input data which doesn't belong to the support of the distribution? E.g. I want to ...
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37 views

Probability of a point fitting a line

I am trying to classify between two groups a set of points given two variables (size of the space = L and points of the space occupied = N). At the moment I have a sample size of 620 samples with ...
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9 views

Reasonableness of a “fit” with more free parameters than fit targets?

I have a (physics) model with 19 free parameters, but only 12 experimental values (= fit targets) that need to be reproduced by the model. This be more precise: 19 parameters are put into ...
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15 views

Explanatory power of variable

To clarify from the very beginning, I expect relations between my variables to be very non-linear, so usual correlation and PCA approach may not work here. Also, for simplicity all the variables are ...
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13 views

Best-fit plane for a set of points

I have a set of 3D points, ie: $P\{(x_1, y_1, z_1), ..., (x_N, y_N, z_N)\}$. Each point in the set is a stellar object, and the $(x,y,z)$ system is defined from their equatorial coordinates and ...
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71 views

Fit generalised extreme event distribution in MATLAB/R

I have a location-scale t-student distribution $X$ $$ f(x,\mu,\sigma,\nu) = \frac{1}{\sigma} \frac{\Gamma(\frac{\nu+1}{2})}{\sqrt{\pi\nu} \Gamma (\frac{\nu}{2})} \left( 1 + \frac{(x - ...
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39 views

Data Fitting using R Code

I'm trying to use a copula function but I do not have the equation for my data, I just have all my raw data. Since my data is not normal, I tried fitting it into a normal distribution using the ...
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0answers
14 views

interpretation of inconsistent CFA fit indices

I'm working on a CFA seeking to assess the factor structure of an "improved" version of a personality questionnaire in a new sample. N = 225. Fit indices for the hypothesized two-factor structure ...
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29 views

How to improve the model of a fit to a sinus modulated sinus

I am trying to determine the amplitude of a sinus modulated sinus as accurate as possible. My sampling frequency is sufficently high and I am currently using a LSQ fit. The entire model looks as ...
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1answer
42 views

Two models of different data (sub)sets significantly different?

I need to see if different fits of different data sets are significantly different, preferrably in R. I have sample series A, B and C. These are different in length and all contain variables n, m, o ...
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1answer
58 views

Forecasting and making sense of data

This might seem very elementary or even silly, but all comments are much appreciated. As science major I do not have deep technical knowledge in statistics, so any guidance is much appreciated. Say ...
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1answer
125 views

R: How to estimate the parameters of a Gamma distribution, knowing the empirical cumulative distribution

I have been given an empirical cumulative distribution, and I need to fit a Gamma distribution to it using R. By trial-and-error (and using Excel's Solver), I know that's possible, but I need to ...
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1answer
27 views

Fit distribution to grouped data with unequal intervals

From a social network survey (name generator and name interpretor) I have data about frequencies of interaction ("How often are you in contact with person X?") on a scale I would interpret as interval ...
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1answer
81 views

Rule of thumb for choosing best fit indeces in cfa

I read this intetesting page about fit indices in SEM. There are lot. It seems that the RMSEA is one you should always report, but how to choose the other ones? Is there some kind of rule of thumb? ...
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1answer
58 views

Right skewed asymmetric Gaussian-like distribution

I am trying to find a possible candidate as a fitting function for a distribution that looks like the following I know that this isn't a straightforward question, but I would like a simple function ...
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0answers
14 views

Choosing correct (or at least precise) order of Fourier series

I'm currently trying to learn to analyse periods of certain variable stars using their magnitudes. I stumbled upon a tool that analyse and calculate the periods using the data set supplied but there's ...
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0answers
50 views

Mixture of beta distrubutions

I have data; one column and 310 rows. When I plot the histogram, it has two peaks; see the figure. I would like to find appropriate distribution that fits the data. I tried to mixtools in R, but it ...
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13 views

Basis for fitting a complete monotone

I have set of measured data: x=[x1,x2,....,xn] y=[y1,y2,....,yn] It is a multi component data. However I need to fit for only one component which is known to ...
3
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1answer
91 views

How to measure the goodness-of-fit of a nonlinear model?

Well… I did search for a while before asking and noticed perhaps my question itself has something basically wrong after reading this and this but still not sure so decided to cry out loud :). As ...
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2answers
375 views

Regression: Scatterplot with low R squared and high p-values

Based on three datasets, I have produced the scatterplot below in Python: I am trying to fit a line on each dataset, but when I check the metrics this is what I get: Set 1 (red): R squared=0.002, ...